1 - 2i 2 + i + 4 - i 3 + 2i = - Vidyadip

MCQ

$\frac{{1 - 2i}}{{2 + i}} + \frac{{4 - i}}{{3 + 2i}} = $

A
$\frac{{24}}{{13}} + \frac{{10}}{{13}}i$
B
$\frac{{24}}{{13}} - \frac{{10}}{{13}}i$
C
$\frac{{10}}{{13}} + \frac{{24}}{{13}}i$
✓
$\frac{{10}}{{13}} - \frac{{24}}{{13}}i$

✓

Answer

Correct option: D.

$\frac{{10}}{{13}} - \frac{{24}}{{13}}i$

d
(d) $\frac{{1 - 2i}}{{2 + i}} + \frac{{4 - i}}{{3 + 2i}} = \frac{{(1 - 2i)(3 + 2i) + (4 - i)(2 + i)}}{{(2 + i)(3 + 2i)}}$
$ = \frac{{50 - 120i}}{{65}} = \frac{{10}}{{13}} - \frac{{24}}{{13}}i$.

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "M.C.Q (1 Marks)" from STD 11 - 4.1 complex nubers→STD 11 - 4.1 complex nubers — all question types→Maths STD 11 Science question papers→CBSE Board STD 11 Science question papers→CBSE Board question paper generator→

Similar questions

Find the value of $\lim\limits_{\text{x} \rightarrow 0} \frac{2\text{x}^2 + 3\text{x} + 4}{2}$

Let $S=\{1,2,3, \ldots, 2022\}$. Then the probability, that a randomly chosen number $n$ from the set $S$ such that $\operatorname{HCF}( n , 2022)=1$, is.

The equation of the straight line passing through the point $(3, 2)$ and perpendicular to the line $y = x$ is:

If $\omega ( \ne 1)$is a cube root of unity and ${(1 + \omega )^7} = A + B\omega $, then $A$ and $B$ are respectively, the numbers

The vertex of parabola ${(y - 2)^2} = 16(x - 1)$ is

If the equstion $\text{a}_\text{n}\text{x}^\text{n}+\text{a}_\text{n-1}\text{x}^\text{n-1}+...+\text{a}_1\text{x}=0,$
$\text{a}_1\neq0,\text{n}\geq2,$ has positive root $\text{x}=\alpha$ then the eqestions
$\text{na}_\text{n}\text{x}^\text{n-1}+(\text{n-1})\text{a}_\text{n-1}\text{x}^\text{n-2}+...+\text{a}_1=0$ has a positive root, which is:

If the relation $R : A \rightarrow B,$ where $A = \{1, 2, 3, 4\}$ and $B = \{1, 3, 5\}$ is defined by $\text{R} =\{(\text{x, y}) : \text{x} < \text{y}, \text{x } \text{iA}, \text{y} \in \text{B}\},$ then $R^{-1}\text{OR}$ is:

If $\frac{3+2 \sin \theta}{1-2 \sin \theta}$ is a real number and $0<\theta<2 \pi$, then $\theta=$

Let the set $\mathrm{S}=\{2,4,8,16, \ldots . .512\}$ be partitioned into $3$ sets $A, B, C$ with equal number of elements such that $\mathrm{A} \cup \mathrm{B} \cup \mathrm{C}=\mathrm{S}$ and $\mathrm{A} \cap \mathrm{B}=\mathrm{B} \cap \mathrm{C}=\mathrm{A} \cap \mathrm{C}=\phi$. The maximum number of such possible partitions of $S$ is equal to :

Given six line segments of lengths $2, 3, 4, 5, 6, 7$ units, the number of triangles that can be formed by these lines is